How do we restore only the tax deduction and not pass the rest of the BBB?
You contact your representatives in Congress (mail, phone, in person at town halls and such) and say "hey, stop passing giant omnibus bills". You encourage others to do the same. That's all you can do, as a citizen.
Unfortunately it won't make a difference because the vast majority of Americans simply do not care. So very few people will be putting pressure on their representatives, and nothing will change.
You don't. That's how bills are passed: everyone adds a little of what they want. To the extreme, it's called "pork barrel politics", but there's a whole continuum between that and a basic compromise.